Proposition 1.1 De Moargans Laws

Example: Samples and VariablesFor each of the following, identify the variable(s) of interest, the type of variable, the observational unit (or case) and the sample size.Number of petals of 20 rose flowersSurvey question about whether to have more student apartments in West Lafayette received from 100 households of residents in West Lafayette.Gender and weight of 10 babies born at St. Elizabeth East.Example 2.2.4: Liter Size of Sows A group of 36 2-year-old sows of the same breed were bred. the number of piglets surviving to 21 days of age were recorded for each sow.

What type of variable is this?

Example 2.2.4: Liter Size of Sows (cont)

Example: Bar GraphExample 2.2.4: Liter Size of Sows (Ex.2.2.4.sas)data sow;infile 'I:\My Documents\Stat 503\Ex.2.2.4.dat'; input piglets; run;proc print data=piglets;run;

title1 'Surviving Piglets';proc univariate data=sow noprint;histogram piglets / endpoints = 5 to 15 by 1; run;quit;XExample 2.2.4: Liter Size of Sows (cont)

XExample 2.2.4: Liter Size of Sows (cont)

Example 2.2.4: Liter Size of Sows (cont)

Example 2.2.4: Liter Size of Sows (cont)

Rel. Frequency0.02800.0560.0830.0830.250.2220.1390.0830.056Example 2.2.4: Liter Size of Sows (cont)

Example: Abundance of desert bird speciesHow many species are common in nature and how many are rare? The following frequency distribution is the number of breeding birds of different species in the Organ Pipe Cactus National Monument in southern Arizona.The Analysis of Biological Data, Whitlock, Schluter, 2009, Roberts and Company, pp. 27-29Example: Abundance of desert bird species(Exhistogram.sas)Table CODE:

data abundance;infile 'I:\My Documents\Stat 503\Exhistogram.dat'; input species $ abundance; run;proc print data=abundance;run;

title1 'Relative Percentage of Species';proc univariate data=abundance noprint;histogram abundance / endpoints = 0 to 650 by 50; run;quit;X

Example: Abundance of desert bird speciesTableHistogram

Shapes of Histograms

Sources of Error: Serum ALTAlanine aminotransferase (ALT) is an enzyme found in most human tissues. A study was performed to determine the concentration of serum ALT (U/L) in 129 adult volunteers.

Example: Median and MeanCalculate the median and mean for the following:Example 2.3.1/3: Weight Gain of Lambs11 13 19 2 10 1Example 1: 2.45 2.57 2.81 2.37 2.01Example 2: 2.86 2.65 2.75 2.60 2.30 2.49Example: Median and MeanCalculate the median and mean for the following:Example 2.3.1/2/3: Weight Gain of Lambs11 13 19 2 10 1Example 1: 2.45 2.57 2.81 2.37 2.01Example 1a: 2.45 2.57 2.81 2.37 2.31Example 2: 2.86 2.65 2.75 2.60 2.30 2.49Example 2.3.1/3: (cont)

Mean vs. Median

yyyyyyExample: MenarcheAs part of a larger study of the effects of strenuous exercise on human fertility and fecundity, the ages (in years) of menarche (the beginning of menstruation) for 10 Olympic female endurance athletes (runners and swimmers) who had vigorously trained for at least 18 months prior to menarche were recorded.

What are median, Q1, Q3, IQR?13.613.914.014.214.915.015.015.115.416.4Example: Menarche (ExHistogramM.sas)Q1Q3mean13.613.914.014.214.915.015.015.115.416.4

Q3Example: Menarche (ExHistogramM.sas)

Example: Modified Boxplot

Example 2.5.1/2: Categorical-Categorical RelationshipsIn an effort to determine if there are difference in primary sources of fecal contamination at different locations in the Morro Bay watershed, n = 623 water specimens were collected at three primary locations that feed into Morro Bay: Chorro Creek (n1 = 241), Los Osos Creek (n2 = 256), and Baywood Seeps (n3 = 126). The type of E. Coli strain was identified as Bird, Domestic Pet, Farm animal, Human, or Terrestrial mammal.Example 2.5.1: (cont)

Example 2.5.1: (cont)

Example 2.5.1: (ExHistogramRel.sas)

XExample 2.5.2

Example: 2.5.2: (cont)

Example 2.5.3: Numeric-Categorical RelationshipsThe effect of different lighting conditions on radish shoot growth.

Example 2.5.4: Numeric-Numeric RelationshipsThe relationship between the concentrations of Selenium in tooth and liver for 10 beluga whales.

Example 2.5.4: (cont)

Interpretation of s

Example: Measures of DispersionExample 1: 2.45 2.57, 2.81 2.37 2.01

Calculate: range, IQR, s, variance, coefficient of variation

Example (ExDispersion.sas)Determine the percentage of data points within 1 SD? 2 SD? 7211241612101361313131218151636911Example: Linear TransformationAfter taking the temperature of a large number of healthy adults, it has been determined that the average temperature is = 98.6 F with a SD of s = 0.9 F, and variance of s2 = 0.81 F2What are the mean, SD and variance in Celsius?What are the mean, SD and variance of the standardized temperature,

Example: PopulationsGiven the following samples, what would possible populations be?1) fallen cats brought to one veterinary clinic in NYC.2) 50 children in Vancouver, Canada, suffering from asthma3) a bar in West Lafayette full of voters4) fruit flies trapped at a garbage dump

Example: MenarcheAs part of a larger study of the effects of strenuous exercise on human fertility and fecundity, the ages (in years) of menarche (the beginning of menstruation) for 10 Olympic female endurance athletes (runners and swimmers) who had vigorously trained for at least 18 months prior to menarche were recorded.13.6, 13.9, 14.0, 14.2, 14.9, 15.0, 15.0, 15.1, 15.4, 16.4Draw the stem-and-leaf diagram of this data.xExample: Menarche13.6, 13.9, 14.0, 14.2, 14.9, 15.0, 15.0, 15.1, 15.4, 16.4xExample 2.46: Sucrose ConsumptionThe following are the histograms, means and SD for the amount of sucrose that the black blowfly can drink in 30 mins for different samples sizes.xExample 2.46: Sucrose Consumption

n204010040090015.514.714.315.014.9s6.55.95.05.45.4

x